Question: If X is exponential with rate , find P{[X] = n,X [X] x}, where [x] is defined as the largest integer less than

If X is exponential with rate λ, find P{[X] = n,X − [X] ≤ x}, where [x] is defined as the largest integer less than or equal to x. Can you conclude that [X] and X − [X] are independent?

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